editing disabled

The temperaments listed are 34edo-distinct, meaning that they are all different even if tuned in 34edo. The ordering is by increasing complexity of 5. The temperament of lowest TE complexity supported by the patent val was chosen as the representative for each class of edo-distinctness.

5-limit temperaments

Period generator
Wedgie
Name
Complexity
Commas
34 11
<<8 1 -17]]
Würschmidt
3.958
393216/390625
17 6
<<18 -2 -45]]

9.648
35184372088832/34332275390625
34 15
<<10 -3 -28]]
Mabila
5.755
268435456/263671875
17 3
<<2 -4 -11]]
Srutal
2.121
2048/2025
34 9
<<6 5 -6]]
Hanson
2.685
15625/15552
17 2
<<14 6 -23]]
Vishnu
6.423
6115295232/6103515625
34 13
<<12 -7 -39]]

7.718
549755813888/533935546875
17 7
<<30 8 -57]]

14.26
945539748965690376192/931322574615478515625
34 5
<<4 9 5]]
Tetracot
2.783
20000/19683
17 8
<<22 24 -13]]

10.198
2384185791015625/2313662762852352
34 1
<<14 23 4]]

7.688
97656250000/94143178827
17 1
<<6 22 21]]

6.749
32768000000/31381059609
34 7
<<2 13 16]]
Immunity
4.157
1638400/1594323
17 4
<<10 14 -1]]
Fifive
5.041
9765625/9565938
34 3
<<16 19 -7]]

7.583
152587890625/148769467776
17 5
<<26 16 -35]]
Quatracot
11.648
1490116119384765625/1479074071160291328
2 1
<<0 17 27]]

5.984
134217728/129140163

7-limit temperaments

Period generator
Wedgie
Name
Complexity
Commas
34 11
<<8 1 21 -17 11 46]]

5.146
875/864 6272/6075
17 6
<<16 2 8 -34 -32 13]]

6.478
49/48 393216/390625
34 15
<<10 -3 5 -28 -20 20]]

4.693
49/48 28672/28125
17 3
<<2 -4 -16 -11 -31 -26]]
Diaschismic
4.290
126/125 2048/2025
34 9
<<6 5 3 -6 -12 -7]]
Keemun
2.280
49/48 126/125
17 2
<<14 6 24 -23 -1 39]]

6.227
875/864 19208/18225
34 13
<<12 27 23 15 3 -22]]

6.930
1029/1000 6860/6561
17 7
<<4 -8 2 -22 -8 27]]

3.533
49/48 2048/2025
34 5
<<4 9 19 5 19 19]]

3.995
126/125 2240/2187
17 8
<<22 24 28 -13 -17 -2]]

8.428
126/125 4117715/3779136
34 1
<<14 23 7 4 -28 -48]]

6.799
49/48 546875/531441
17 1
<<6 22 20 21 15 -15]]

5.832
1029/1000 2240/2187
34 7
<<2 13 1 16 -4 -34]]

3.651
49/48 2240/2187
17 4
<<10 14 22 -1 7 12]]

4.891
126/125 6860/6561
34 3
<<16 19 25 -7 -5 5]]

6.502
126/125 84035/78732
17 5
<<8 18 4 10 -16 -41]]

4.958
49/48 20000/19683
2 1
<<0 17 17 27 27 -8]]

5.514
1029/1000 5120/5103